16 Oct '08 16:03

That's the question! I think this one was actually posed in the body of another thread, but let's make the request formal:

The question itself is a little confusing, so I'll provide a few examples. If there are 2 people in the group, here are the possible responses:

(0,0)

(1,0)

(0,1)

(1,1)

(2,0)

(0,2)

(2,1)

(1,2)

(2,2)

If both answer "2", i.e. (2,2), then both people are correct. If either player answers "1" and the other does not, i.e. (1,0), (1,2), (0,1), (2,1), then the player that answered "1" is correct. If both players answer "0", i.e. (0,0), then the result is undecidable because of the following logic loop: neither player answered "2", which means both were wrong, which means the correct answer is "0", but both players answered "0" which means that both players were right, but neither player actually answered "2", which means that... (etc...). Similar undecidable situations arise with the other answers, and in larger groups where there are multiple correct answer clusters (which, funnily enough, means that 2 rights make a wrong!).

Hopefully the question makes sense, and we come up with an answer that also makes sense. Enjoy!

**If you ask a group of "n" people "how many people in this group will answer this question correctly?", what is the probability that the question will be answered correctly by "m" people?**The question itself is a little confusing, so I'll provide a few examples. If there are 2 people in the group, here are the possible responses:

(0,0)

(1,0)

(0,1)

(1,1)

(2,0)

(0,2)

(2,1)

(1,2)

(2,2)

If both answer "2", i.e. (2,2), then both people are correct. If either player answers "1" and the other does not, i.e. (1,0), (1,2), (0,1), (2,1), then the player that answered "1" is correct. If both players answer "0", i.e. (0,0), then the result is undecidable because of the following logic loop: neither player answered "2", which means both were wrong, which means the correct answer is "0", but both players answered "0" which means that both players were right, but neither player actually answered "2", which means that... (etc...). Similar undecidable situations arise with the other answers, and in larger groups where there are multiple correct answer clusters (which, funnily enough, means that 2 rights make a wrong!).

Hopefully the question makes sense, and we come up with an answer that also makes sense. Enjoy!